1. Field of the Invention
The present invention relates to Fabri-Perot spectroscopy method and Fabri-Perot spectroscopy apparatus utilizing the same, and more particularly to Fabri-Perot spectroscopy method and apparatus having a high spectroscopy resolution by passing a light beam containing multi-wavelength through a Fabri-Perot interference plate a plurality of times to expand an interval between adjacent wavelengths of the light to be spectroscopied.
2. Related Background Art
Of various spectroscopy methods, a Fabri-Perot spectroscopy method has been well known as a spectroscopy method having a high wavelength resolution.
FIG. 1 shows a basic principle of the Fabri-Perot spectroscopy method.
Numerals 1 and 3 denote high reflection films, numerals 2 and 4 denote glass plates, numeral 5 denotes an incident light and numeral 6 denotes a transmitted light. In the Fabri-Perot spectroscopy method, the glass plate 2 having the high reflection film 1 formed thereon and the glass plate 4 having the high resolution film 3 formed thereon are arranged in parallel with a spacing h therebetween to form a Fabri-Perot interference plate.
A spectroscopy transmitted light 6 produced when the incident light 5 having various wavelengths is applied to the Fabri-Perot interference plate at a predetermined incident angle is given by the following formula. A transmission factor T which is a ratio of a transmitted light intensity I.sup.(t) to an incident light intensity I.sup.(i) of a wavelength .lambda..sub.0 is ##EQU1## where n' is a refraction coefficient of a medium, .theta.' is a refraction angle in the medium n', and R is a reflection coefficient of the high reflection films 1 and 2. (See "Principles of Optics" 3rd Edition, M. Born and E. Wolf, Pergamon Press, 1965, page 327.)
When the spacing h and the refraction angle .theta.' are constant, the transmission factor T to wavelengths .lambda..sub.N-1, .lambda..sub.N and .lambda..sub.N+1 are shown in FIG. 2. As seen from the formula (1), T is a periodic function of .delta.. In the formula (2), when .delta.=2.pi.N (where N is an integer), T is maximum and the light having the wavelength .lambda..sub.0 =.lambda..sub.N is transmitted.
When n'=1, the formula (2) is rewritten as ##EQU2## and the transmitted light .lambda..sub.N is given by ##EQU3## When h=10 mm and .theta.'=0, .lambda..sub.N is given by Table 1.
TABLE 1 ______________________________________ N(integer) .lambda..sub.N (.mu.m) ______________________________________ 39,998 0.5000250 39,999 0.5000125 40,000 0.5000000 40,001 0.4999875 40,002 0.4999750 ______________________________________
When h=1.6.times.10.sup.-3 mm and .theta.'=0.degree., .lambda..sub.N is given by Table 2.
TABLE 2 ______________________________________ N .lambda..sub.N (.mu.m) ______________________________________ 4 0.80000 5 0.64000 6 0.53333 7 0.45714 8 0.40000 ______________________________________
It is seen that the interval between adjacent wavelengths significantly varies with the spacing h. For example, the interval between wavelengths is 0.0000125 .mu.m (=0.0125 nm) in the Table 1, and it is 0.07619 .mu.m (difference between wavelengths for N=6 and N=7) in the Table 2.
A wavelength resolution is given by a finess F which is a ration of the difference between adjacent wavelengths and a half-amplitude width .DELTA..lambda..sub.N. That is, the finess F is given by ##EQU4## The finess F is determined by F' of the formula (3), and F is determined by a reflection coefficient R. Thus, the finess F is determined by the reflection coefficient R. For example, when R=0.95, EQU F=61.2
and when the spacing h=10 mm, the wavelength resolution is 0.0125 .mu.m/61.2=0.0002 nm, and when the spacing h=1.6.times.10.sup.-3 mm, it is 0.07619 (.mu.m)/61.2=0.0012 .mu.m =1.2 nm. In any case, the resolution is very high. On the other hand, the interval between the adjacent wavelengths is small and the wavelength band of the spectroscopy apparatus is narrow.
In FIG. 3, in order to resolve the above problem, the apparatus is combined with another spectrometer (prism spectrometer) to measure a specific wavelength with a high resolution. (See "Principles of Optics", 3rd Edition, M. Born and E. Wolf, Pergamon Press, 1965, page 336.)
In FIG. 3, numeral 7 denotes a light source, numeral 8 denotes a collimeter lens, numeral 9 denotes a Fabri-Perot interference plate, numeral 10 denotes a focusing lens, numeral 11 denotes a pinhole, numeral 12 denotes a collimeter lens, numeral 13 denotes a prism, numeral 14 denotes a focusing lens, and numeral 15 denotes a view plane.
A light emitted from the light source is collimated by the collimeter lens 8, spectroscopied by the Fabri-Perot interference plate 9 and focused on the pinhole 11 by the focusing lens 10. The lights other than that on an optical axis is blocked by the pinhole 11 and the remaining light is recollimated by the collimeter lens 12, passes through the prism 13 where outlet angle is changed with the wavelength, and the light is focused by the focusing lens 14 on the view plane 15 on which focusing points for individual wavelengths are positionally separated. In this manner, the adjacent wavelengths are separated.
However, in this method, it is necessary to use the other spectroscopy method, that is, the prism spectroscopy method, and troublesome optical axis alignment and correction of aberration are required to match the spectrometers.
Accordingly, a practical Fabri-Perot spectroscopy method is limited to measurement of a longitudinal mode of a laser beam having a narrow spectrometric band.